Class 8 Mathematics Chapter 8 Algebraic Expressions and Identities

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I. Chapter Summary:

This chapter introduces students to the world of algebraic expressions involving variables and constants, with operations such as addition, subtraction, and multiplication. It also builds foundational knowledge of identities—equations that hold true for all values of variables. The chapter focuses on expanding and factorizing expressions using identities and simplifies algebraic manipulation, which prepares students for advanced algebra in higher classes.

II. Key Concepts Covered:

Concept	Explanation
Algebraic Expressions	Expressions made up of variables, constants, and mathematical operations (+, –, ×).
Terms of an Expression	Parts separated by + or – in an expression. Each term has a coefficient and literal part.
Like and Unlike Terms	Terms with same variable parts and powers are like terms; others are unlike terms.
Addition and Subtraction of Algebraic Expressions	Combining like terms to simplify.
Multiplication of Algebraic Expressions	Using distributive property to multiply monomials, binomials, trinomials.
Standard Identities	Important identities used to simplify algebraic expressions:

$a + b)^2 = a^2 + 2ab + b^2$
$a – b)^2 = a^2 – 2ab + b^2$
$a^2 – b^2 = (a + b)(a – b)$ |

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

The product of $3 x$ and $4 x$ is:
a) 12x²
b) 7x
c) 12x
d) 3x²
Answer: a) 12x²
Which of the following is a binomial?
a) $x$
b) $2 x + 3$
c) $x^2 + 2x + 1$
d) 7
Answer: b) $2 x + 3$
(PYQ 2021) If $a = 2$ and $b = 3$ , then value of $a + b)^2$ is:
a) 25
b) 30
c) 36
d) 20
Answer: a) 25
Which identity is used in the expansion of $2x + 3)^2$ ?
a) $a^2 – b^2$
b) $a + b)^2$
c) $a – b)^2$
d) None
Answer: b) $ $a + b)^2$

(B) Short Answer Questions (2–3 Marks)

Simplify: $3 x + 5 y - 2 x + 7 y$
Multiply: $2 x (x + 5)$
Factorize: $x^2 – 9$ using identity.
(PYQ 2020) Expand: $a – 2)^2$

(C) Long Answer Questions (5 Marks)

Expand using identity: $3x + 4)^2$ and verify by direct multiplication.
Multiply: $(2 x + 3) (2 x - 3)$ and state the identity used.
Simplify: $x2+5x+6+2×2−3x+4x^2 + 5x + 6 + 2x^2 – 3x + 4$
(PYQ 2019) Factorize: $x^2 – 6x + 9$

(D) HOTS (Higher Order Thinking Skills)

The product of two binomials is $x^2 + 5x + 6$ . Find the binomials.
Prove that for any two numbers $a$ and $b$ , $a + b)^2 – (a – b)^2 = 4ab$

IV. Key Formulas/Concepts

Concept	Formula/Example
Addition of Expressions	Combine like terms: $3 x + 2 y + 5 x = 8 x + 2 y$
Multiplication (Monomial × Monomial)	$a^m × a^n = a^{m+n}$
Identities

$a + b)^2 = a^2 + 2ab + b^2$
$a – b)^2 = a^2 – 2ab + b^2$
$a^2 – b^2 = (a + b)(a – b)$ |
| Algebraic expression types | Monomial, Binomial, Trinomial, Polynomial |

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

Unit/Chapter	Estimated Marks	Type of Questions Typically Asked
Algebraic Expressions & Identities	7–9 Marks	MCQs, Simplification, Expansion, HOTS

VII. Previous Year Questions (PYQs)

Year	Marks	Question
2021	1 mark	Value of $a + b)^2$ when $a = 2, b = 3$
2020	3 marks	Expand $a – 2)^2$ using identity
2019	5 marks	Factorize $x^2 – 6x + 9$
2018	2 marks	Multiply $2 x (x + 5)$

VIII. Real-World Application Examples:

Engineering & Architecture: Algebraic expressions help in design models, building formulas.
Physics Formulas: Kinetic energy $=12mv2=\frac{1}{2}mv^2$ is algebraic.
Finance & Accounting: Profit/loss expressions use variables like cost, selling price, tax.
Coding & Computer Science: Variables and expressions form the base of algorithms.

IX. Student Tips & Strategies for Success (Class 8 Specific)

Time Management:

Dedicate 20 minutes daily to algebra practice.
Use flashcards for memorizing identities.

Exam Preparation:

Practice identity-based questions regularly.
Don’t skip solving expansions and factorizations by both identity and normal method.

Stress Management:

Practice with music or visual aids to ease math anxiety.
Use math apps or games for engaging practice.

X. Career Guidance & Exploration

For Classes 9–10:

Streams Overview: Algebra is critical for Science and Commerce.
NTSE, Olympiads: Algebra questions are common.
Explore Early Careers: Engineering, Chartered Accountancy, Data Science require strong algebra skills.

For Classes 11–12:

Algebra is the foundation for JEE, NEET, CUET and further math applications in:
- Engineering
- Architecture
- Economics
- Physics
- Machine Learning and AI

XI. Important Notes

Regular practice improves algebra fluency—aim for 10 questions a day.
Master the three standard identities—they appear repeatedly.
Always double-check signs (+/–) while expanding and factorizing.

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